Geometry
Area from a base and its perpendicular height
The standard form. Multiply the two lengths first and halve afterwards, so the intermediate figure can be compared with the bounding parallelogram.
The Formula
A = 1/2 x base x height
The standard form. Multiply the two lengths first and halve afterwards, so the intermediate figure can be compared with the bounding parallelogram.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| b | Base — any one side you choose | length | Any of the three sides works; the area is unchanged by the choice. |
| h | Perpendicular height to that base | length | Shortest distance to the opposite corner. Never the length of a slanted side, and it may fall outside the triangle. |
| A | Enclosed area | square units | Half of the parallelogram on the same base and height. |
What Each Symbol Means
blength
Base — any one side you choose
Any of the three sides works; the area is unchanged by the choice.
hlength
Perpendicular height to that base
Shortest distance to the opposite corner. Never the length of a slanted side, and it may fall outside the triangle.
Asquare units
Enclosed area
Half of the parallelogram on the same base and height.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the area of a triangle page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Area Of A Triangle, filed under Math. Every number the guide produces comes from substituting into this one line.